Finite Group Databasebeta

← C11×#12275 #14589468

Subgroups — C11×#12275 #14589468

Order 2816.

372 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2832C211yesmaximal, characteristic
2C11×#2028C211yesmaximal, characteristic, complemented
3C11×#1605C211yesmaximal, characteristic, complemented
4C11×#1599C211yesmaximal, characteristic
5C11×#1354C211yesmaximal, characteristic, complemented
6C11×#1345C211yesmaximal, characteristic
7C11×#1319C211yesmaximal, characteristic, complemented
8C11×#544C2211yescharacteristic
9C11×#451—21no—
10C11×#450—21no—
11C11×#419—21no—
12C11×#400—21no—
13C11×#397—21no—
14C11×#395C2211yescharacteristic
15C11×#394—21no—
16C11×#394C2211yescharacteristic
17C11×#393—21no—
18C11×#393—21no—
19C11×#391C2211yescharacteristic
20C11×#388—21no—
21C11×#343C2211yescharacteristic
22C11×#339—21no—
23C11×#328—21no—
24C11×#328—21no—
25C11×#324C2211yescharacteristic
26C11×#324C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C22×D4×C11D411yescharacteristic
30C2×C11×Q16—41no—
31C2×C11×SD16—41no—
32C2×C11×M16—21no—
33C11×C4⋊Q8—41no—
34C11×#125—41no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×#117—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2311yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C42×C11D411yescharacteristic
48C11×#103—41no—
49C11×#103—41no—
50C11×#103—41no—
51C11×#102—41no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95D411yescharacteristic
61C11×#95D411yescharacteristic
62#12275C1111yesmaximal, characteristic, direct product factor, Sylow
63C24×C11—21no—
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—81no—
72C2×D4×C11—41no—
73C2×D4×C11—81no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C11×Q16—82no—
83C11×SD16—82no—
84C11×M16—41no—
85C11×M16—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—81no—
97C11×C4⋊C4—81no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—81no—
102C11×C22⋊C4—81no—
103C11×C22⋊C4—81no—
104C11×C22⋊C4—81no—
105C11×C22⋊C4—81no—
106C42×C11—41no—
107C42×C11—41no—
108#2832C2×C1111yescharacteristic
109#2028C2×C1111yescharacteristic, complemented
110#1605C2×C1111yescharacteristic, complemented
111#1599C2×C1111yescharacteristic
112#1354C2×C1111yescharacteristic, complemented
113#1345C2×C1111yescharacteristic
114#1319C2×C1111yescharacteristic, complemented
115C23×C11—41no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123Q8×C11—42no—
124Q8×C11—42no—
125Q8×C11—81no—
126Q8×C11—81no—
127Q8×C11—81no—
128Q8×C11—81no—
129D4×C11—42no—
130D4×C11—81no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C8×C11—81no—
157C8×C11—81no—
158C8×C11—81no—
159#544C22×C1111yescharacteristic
160#451—21no—
161#450—21no—
162#419—21no—
163#400—21no—
164#397—21no—
165#395C22×C1111yescharacteristic
166#394—21no—
167#394C22×C1111yescharacteristic
168#393—21no—
169#393—21no—
170#391C22×C1111yescharacteristic
171#388—21no—
172#343C22×C1111yescharacteristic
173#339—21no—
174#328—21no—
175#328—21no—
176#324C22×C1111yescharacteristic
177#324C22×C1111yescharacteristic
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—81no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11#45211yescharacteristic
188C22×C11#45511yescharacteristic
189C22×C11B(4,𝔽2)11yescharacteristic
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—81no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198C4×C11—81no—
199C4×C11—81no—
200C4×C11—81no—
201C22×Q8D4×C1111yescharacteristic
202C22×Q8D4×C1111yescharacteristic
203C22×D4D4×C1111yescharacteristic
204C2×Q16—41no—
205C2×SD16—41no—
206C2×M16—21no—
207C4⋊Q8—41no—
208#125—41no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211#117—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C23×C1111yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C42D4×C1111yescharacteristic
222#103—41no—
223#103—41no—
224#103—41no—
225#102—41no—
226C22⋊C8—21no—
227C22⋊C8—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95D4×C1111yescharacteristic
235#95D4×C1111yescharacteristic
236C2×C11—21no—
237C2×C11—21no—
238C2×C11—161no—
239C2×C11#160611yescharacteristic
240C2×C11#219911yescharacteristic
241C2×C11#220311yescharacteristic
242C24—21no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—81no—
251C2×D4—41no—
252C2×D4—81no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4C2×D4×C1111yescharacteristic
259C22×C4C2×D4×C1111yescharacteristic
260C22×C4C2×D4×C1111yescharacteristic
261Q16—82no—
262SD16—82no—
263M16—41no—
264M16—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C22⋊C4—81no—
283C22⋊C4—81no—
284C22⋊C4—81no—
285C42—41no—
286C42—41no—
287C11#1227511yescharacteristic, direct product factor, Sylow
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23C11×#12011yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—81no—
299Q8—81no—
300Q8—81no—
301Q8—81no—
302D4—42no—
303D4—81no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4C11×#13511yescharacteristic
328C2×C4C11×#13711yescharacteristic
329C8—81no—
330C8—81no—
331C8—81no—
332C22—21no—
333C22—21no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22C11×#45211yescharacteristic
342C22C11×#45511yescharacteristic
343C22C11×B(4,𝔽2)11yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—81no—
354C4—81no—
355C2—21no—
356C2—21no—
357C2—161no—
358C2C11×#160611yescharacteristic
359C2C11×#219911yescharacteristic
360C2C11×#220311yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C4⋊C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C11×#2028C2semidirect
3. C11×#1605C2semidirect
5. C11×#1354C2semidirect
7. C11×#1319C2semidirect
62. #12275C11direct (N × H)
109. #2028C2×C11semidirect
110. #1605C2×C11semidirect
112. #1354C2×C11semidirect
114. #1319C2×C11semidirect
287. C11#12275direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#28322
C11×#20282
C11×#16052
C11×#15992
C11×#13542
C11×#13452
C11×#13192
#1227511